Polyester polyols, processes for making them, and applications for the polyols are disclosed. Some of the polyols comprise recurring units from a digested thermoplastic polyester (e.g., recycled polyethylene terephthalate), a diol, an optional hydrophobe, and a clarifier. The clarifier, which in some cases is a bisphenol, bisphenol alkoxylate, bisphenol polycarbonate, sulfonyl diphenol, or sulfonyl diphenol alkoxylate, helps the polyol remain clear for weeks or months after its preparation. In some aspects, the clarifier is a monophenol, bisphenol, or poly-phenol having two or more phenylene rings wherein at least two of the phenylene rings lack a common molecular axis. The clarifier may also be an alkylated phenol, an epoxy resin, an epoxy novolac resin, a diphenylmethane, or a tris(aryloxy)phosphate. The polyols are valuable for formulating a variety of polyurethanes and related products—including polyurethane dispersions, flexible and rigid foams, coatings, adhesives, sealants, and elastomers—and they provide a sustainable alternative to bio- or petrochemical-based polyols.